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3 years ago

How does the volume of a cylinder change when it’s diameter is doubled

1 answer:

8 0

Recallin that, the diameter is twice as long as the radius, namely the radius is half the diameter, so, if the diameter is doubled, the radius is also doubled.

$\bf \textit{volume of a cylinder}\\\\
V=\pi r^2 h\quad 
\begin{cases}
r=radius\\
h=height\\
-----\\
r=\stackrel{doubled}{2r}
\end{cases}\implies V=\pi (2r)^2 h
\\\\\\
V=\pi (2^2r^2)h\implies V=\pi 4r^2 h\implies V=4~(\pi r^2 h)$

notice, the new volume is 4 times (πr² h), namely 4 times the original.

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Evaluate using the finite geometric sum formula

Sever21 [200]

Answer:

$S_9=-18.703$ .

Step-by-step explanation:

The given series is,

$\sum_{i=1}^9(-\frac{1}{2})^{i-1}$

When we substitute $i=1$ , we get the first term, which is $a_1=-28(-\frac{1}{2})^{1-1}$

This implies that,

$a_1=-28(-\frac{1}{2})^{0}$

$a_1=-28(1)=-28$ .

The common ratio is

$r=-\frac{1}{2}$

The finite geometric sum is given by the formula,

$S_n=\frac{a_1(r^n-1)}{r-1} , -1\:$ .

Since there are 9 terms, we find the sum of the first nine terms by putting $n=9$ in to the formula to get,

$S_9=\frac{-28((-\frac{1}{2})^9-1)}{-\frac{1}{2}-1}$ .

$S_9=\frac{-28((-\frac{1}{512})-1)}{-\frac{3}{2}}$ .

$S_9=\frac{-28(-\frac{513}{512})}{-\frac{3}{2}}$ .

$S_9=-28(\frac{171}{256})$ .

$S_9=-\frac{1197}{64}$ .

$S_9=-18.703$ .

The correct answer is B

4 0

3 years ago

Read 2 more answers

Help please, 30 points reward, i literally have no clue

Brums [2.3K]

The explanation for this is one of my favorite pieces of mathematical reasoning. First, let's thing about distance; what's the shortest distance between two points? <em>A straight line</em>. If we just drew a straight line between A and B, though, we'd be missing a crucial element of the original problem: we also need to pass through a point on the line (the "river"). Here's where the mathemagic comes in.

If we take the point B and <em>reflect it over the line</em>, creating the point B' (see picture 1), we can draw a line straight from A to B' that passes through a point on the line. Notice the symmetry here; the distance from the intersection point to B' is<em> the same as its distance to B</em>. So, if we reflect that segment back up, we'll have a path to B, and because it came from of the line segment AB', we know that it's <em>the shortest possible distance that includes a point on the line</em>.

If we apply this same process to our picture, we see that the line segment AB' crosses the line $\ell$ at the point (1, 1)

6 0

4 years ago

A vectador is buying two new cowboy hats.All together the hats cost $75.12.The second hat costs twice as more as the first hat.W

faust18 [17]

<h2>Greetings!</h2>

Answer:

$50.08

Step-by-step explanation:

Let x be the cheaper hat, is the more expensive hat is 2 times this value, it can be shown by 2x. The addition of these two values = 75.12

x + 2x = 75.12

3x = 75.12

Divide both sides by three to find 1x:

x = 25.04

If the more expensive hat is 2x this, then:

2 * 25.04 = 50.08

So the more expensive hat is $50.08!

<h2>Hope this helps!</h2>

6 0

3 years ago

Ube had made a banana cream pie. His brother he 1/3 of a pie and his sister had 2/5 of the pie how much less did his brother eat

Dimas [21]

Find the LCD (least common denominator)
15 in this case
Convert to have 15 as denominators

1/3 = 5/15
2/5 = 6/15

Subtract

(6/15) - (5/15)
1/15

He had 1/15 less

7 0

3 years ago

What is the slope of 2x + y = 5

vitfil [10]

2. the slope is 2 because

8 0

4 years ago

Read 2 more answers